Can you find a formula giving the wavelength(λ) as a function of amperage(I)
and induction(L)?

Isn't one wavelength produced by one circuit of the electrons around the coil? I'm a rank amateur at this but I've seen videos of electrons producing waves on youtube. see this video

I would be interested in what the more seasoned physicists have to say but I would guess that the wavelength would be the reciprocal of the electrons per seconds around a coil which would depend on the diameter of the coil and the speed of the electrons.

The value of L for an air-core tightly wind coil with small gauge wire is:

$\displaystyle L = \frac 1 l \mu_0 N^2 A$

where $\displaystyle l $ is the length of the coil, $\displaystyle \mu_0$ is the permeability of free space, which is $\displaystyle \mu_0= 4 \pi \times 10^{-7} H/m$, N is the number of turns of the coil, and A is the cross-sectional area of the coil. Note that neither current nor speed of the electrons has anything to do with this. In fact, the speed of electron flow in a typical electronic circuit like this is really quite small: around 0.002 m/s. Hence radiation due to the electron's circular motion about the coil (known as Synchrotron Radiation) is negligible.

Note that neither current nor speed of the electrons has anything to do with this. In fact, the speed of electron flow in a typical electronic circuit like this is really quite small: around 0.002 m/s. Hence radiation due to the electron's circular motion about the coil (known as Synchrotron Radiation) is negligible.